Data analysis
Answers are for parents and teachers.
1
Classify by scale: (a) the colour of a car, (b) a pupil’s rank in the class, (c) the temperature in °C, (d) the length of a journey in minutes.
(a) nominal, (b) ordinal, (c) interval, (d) ratio.
2
Find the mean, median and mode of 3, 4, 4, 6, 8, 9, 10, 10 (mean first; list is already sorted).
Sum 54, count 8, mean 6.75. Median (6 + 8) ÷ 2 = 7. Modes: 4 and 10.
3
Find the variance and the standard deviation of 1, 5 (mean 3, divide by 2).
Squared distances 4 and 4; sum 8; variance 8 ÷ 2 = 4; standard deviation 2.
4
Using mark = 6 × hours + 41, predict the mark for 5 hours. Is the prediction reliable for 5 hours? And for 20 hours?
6 × 5 + 41 = 71. Yes, 5 is inside the data range 1 to 6. No for 20: it is far outside the range (it gives 161).
5
In a school, the number of umbrellas brought and the number of colds both rise in winter. Does this prove that umbrellas cause colds? Explain in a sentence.
No. Winter weather (rain and cold) causes both; the two only change together.